7.5 Laws of Logarithms

Expand the following logarithm: 
log₂ 5x.

• log₂ 5 - log₂ x 
• log₂ 5 + log₂ x 
• 2log 5 + 2log x
• log5 2 + log_x 2

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Write log_b(x/y) as two logs

• log_bx-log_by
• log_bx+log_by
• log_bx*log_by
• log_bx/log_by

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

Rewrite log_b(xⁿ)

• nlog_bx
• (log_bx)ⁿ
• xⁿlog_bx
• log_b(xⁿ)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

• 6log₈(xyz)
• log₈(x) - log₈(y) - 6log₈(z)
• log₈(x) + log₈(y) - log₈(z)
• log₈(x) + log₈(y) + 6log₈(z)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

• log(x) + log(z) + 4log(y)
• 3log(x) − log(z) − 4log(y)
• 3log(x) + log(z) + 4log(y)
• log(x) − 4log(z) − 3log(y)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Expand

• 6log₈v-2log₈u
• 6log₈u-2log₈v
• 3log₈u-2log₈v
• 6log₈u+2log₈v

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Write as a single log: log 12 + 2 log x

• log (12 + 2x)
• log (14x)
• log (12 * 2x)
• log (12x²)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Simplify: 2log(x) + 3log(xy)

• log(x⁵y³)
• log(5xy)
• 5log(x²y)
• log(6x²y)

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Condense the following logarithm: 3 log₂ x + 2 log₂ y – 4 log₂ z 

• log₂ x³y²∕z⁴
• log₂ x³y²z⁴
• log₂ xyz⁹
• 9log₂ xyz

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

• 5log₆(a) + 6log₆(c) − 30log₆(b)
• log₆(a) + 6log₆(c) − 5log₆(b)
• 6log₆(a) − 6log₆(c) − 30log₆(b)
• 6log₆(a) + 6log₆(c) − 30log₆(b)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5